// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/* This file is a modified version of heap_relax_snode.c file in SuperLU
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 *
 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 *
 * Permission is hereby granted to use or copy this program for any
 * purpose, provided the above notices are retained on all copies.
 * Permission to modify the code and to distribute modified code is
 * granted, provided the above notices are retained, and a notice that
 * the code was modified is included with the above copyright notice.
 */

#ifndef SPARSELU_RELAX_SNODE_H
#define SPARSELU_RELAX_SNODE_H

namespace Eigen {

namespace internal {

/**
 * \brief Identify the initial relaxed supernodes
 *
 * This routine is applied to a column elimination tree.
 * It assumes that the matrix has been reordered according to the postorder of the etree
 * \param n  the number of columns
 * \param et elimination tree
 * \param relax_columns Maximum number of columns allowed in a relaxed snode
 * \param descendants Number of descendants of each node in the etree
 * \param relax_end last column in a supernode
 */
template<typename Scalar, typename StorageIndex>
void
SparseLUImpl<Scalar, StorageIndex>::relax_snode(const Index n,
												IndexVector& et,
												const Index relax_columns,
												IndexVector& descendants,
												IndexVector& relax_end)
{

	// compute the number of descendants of each node in the etree
	Index parent;
	relax_end.setConstant(emptyIdxLU);
	descendants.setZero();
	for (Index j = 0; j < n; j++) {
		parent = et(j);
		if (parent != n) // not the dummy root
			descendants(parent) += descendants(j) + 1;
	}
	// Identify the relaxed supernodes by postorder traversal of the etree
	Index snode_start; // beginning of a snode
	for (Index j = 0; j < n;) {
		parent = et(j);
		snode_start = j;
		while (parent != n && descendants(parent) < relax_columns) {
			j = parent;
			parent = et(j);
		}
		// Found a supernode in postordered etree, j is the last column
		relax_end(snode_start) = StorageIndex(j); // Record last column
		j++;
		// Search for a new leaf
		while (descendants(j) != 0 && j < n)
			j++;
	} // End postorder traversal of the etree
}

} // end namespace internal

} // end namespace Eigen
#endif
